Subgroups — C₄₁×#60963 #23837164

Order 10496.

1804 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3249	C₂	1	2	yes	maximal, complemented
4	C₄₁×#3246	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3238	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3237	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3218	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3216	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3190	C₂	1	4	yes	maximal, complemented
10	C₄₁×#3181	C₂	1	4	yes	maximal, complemented
11	C₄₁×#3116	C₂	1	4	yes	maximal, complemented
12	C₄₁×#3113	C₂	1	2	yes	maximal, complemented
13	C₄₁×#3112	C₂	1	2	yes	maximal, complemented
14	C₂×C₄₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#533	—	2	1	no	—
16	C₄₁×#533	—	2	1	no	—
17	C₄₁×#533	—	2	1	no	—
18	C₄₁×#533	—	2	1	no	—
19	C₄₁×#533	C₂²	1	1	yes	characteristic
20	C₄₁×#533	C₂²	1	2	yes	—
21	C₄₁×#533	C₂²	1	2	yes	—
22	C₄₁×#533	C₂²	1	2	yes	—
23	C₄₁×#533	C₂²	1	2	yes	—
24	C₄₁×#533	C₂²	1	1	yes	characteristic
25	C₄₁×#533	C₂²	1	1	yes	characteristic
26	C₄₁×#532	C₂²	1	1	yes	characteristic
27	C₄₁×#532	C₂²	1	1	yes	characteristic
28	C₄₁×#532	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#529	—	2	1	no	—
32	C₄₁×#529	—	2	1	no	—
33	C₄₁×#529	—	2	1	no	—
34	C₄₁×#529	—	2	1	no	—
35	C₄₁×#529	C₂²	1	2	yes	—
36	C₄₁×#529	C₂²	1	2	yes	—
37	C₂×#125×C₄₁	—	2	1	no	—
38	C₄₁×#525	—	2	1	no	—
39	C₄₁×#525	—	2	1	no	—
40	C₄₁×#525	C₂²	1	2	yes	—
41	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
42	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
43	C₄×#41×C₄₁	—	2	1	no	—
44	C₄×#41×C₄₁	—	2	1	no	—
45	C₄×#41×C₄₁	C₂²	1	2	yes	—
46	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
47	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
48	C₂×#117×C₄₁	—	2	1	no	—
49	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
50	C₄₁×#501	C₂²	1	4	yes	complemented
51	C₄₁×#497	C₂²	1	4	yes	complemented
52	C₄₁×#491	C₂²	1	4	yes	complemented
53	C₄₁×#489	C₂²	1	4	yes	complemented
54	C₄₁×#485	C₂²	1	8	yes	—
55	C₄₁×#483	C₂²	1	4	yes	—
56	C₄₁×#480	C₂²	1	4	yes	—
57	C₄₁×#477	C₂²	1	4	yes	complemented
58	C₄₁×#477	C₂²	1	4	yes	complemented
59	C₄₁×#476	C₂²	1	4	yes	complemented
60	C₄₁×#475	C₂²	1	4	yes	complemented
61	C₄₁×#467	C₂²	1	8	yes	—
62	C₄₁×#465	C₂²	1	8	yes	—
63	C₄₁×#462	C₂²	1	4	yes	complemented
64	C₄₁×#462	C₂²	1	4	yes	complemented
65	C₄₁×#461	C₂²	1	4	yes	complemented
66	C₄₁×#460	C₂²	1	4	yes	complemented
67	C₄₁×#452	C₂²	1	8	yes	—
68	C₄₁×#451	C₂²	1	4	yes	—
69	C₄₁×#448	C₂²	1	4	yes	—
70	C₄₁×#441	C₂²	1	8	yes	complemented
71	C₄₁×#440	C₂²	1	8	yes	complemented
72	C₄₁×#432	C₂²	1	2	yes	—
73	C₄₁×#432	C₂²	1	2	yes	—
74	C₄₁×#432	C₂²	1	2	yes	—
75	C₄₁×#432	C₂²	1	2	yes	—
76	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
77	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
78	C₂×#97×C₄₁	C₂²	1	2	yes	—
79	C₂×#41×C₄₁	—	2	1	no	—
80	C₂×#41×C₄₁	—	2	1	no	—
81	C₂×#41×C₄₁	C₂³	1	2	yes	—
82	C₂²×Q₈×C₄₁	—	2	1	no	—
83	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
84	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
85	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
86	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₄₁	C₂³	1	8	yes	—
88	C₂×SD₁₆×C₄₁	C₂³	1	8	yes	—
89	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
90	C₄⋊Q₈×C₄₁	—	2	1	no	—
91	C₄⋊Q₈×C₄₁	—	2	1	no	—
92	C₄⋊Q₈×C₄₁	—	2	1	no	—
93	C₄⋊Q₈×C₄₁	—	2	1	no	—
94	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
95	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
96	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
97	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
98	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
99	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
101	#127×C₄₁	C₂³	1	1	yes	characteristic
102	#126×C₄₁	—	2	2	no	—
103	#126×C₄₁	—	2	2	no	—
104	#125×C₄₁	—	2	2	no	—
105	#125×C₄₁	—	2	2	no	—
106	#125×C₄₁	—	2	2	no	—
107	#125×C₄₁	—	2	2	no	—
108	#125×C₄₁	—	2	1	no	—
109	#125×C₄₁	—	2	1	no	—
110	#125×C₄₁	C₂³	1	2	yes	—
111	#124×C₄₁	—	2	1	no	—
112	#124×C₄₁	—	2	1	no	—
113	#124×C₄₁	C₂³	1	2	yes	—
114	#123×C₄₁	—	2	2	no	—
115	#123×C₄₁	—	2	2	no	—
116	#123×C₄₁	—	2	2	no	—
117	C₂²⋊Q₈×C₄₁	—	2	2	no	—
118	C₂²⋊Q₈×C₄₁	—	2	2	no	—
119	C₂²⋊Q₈×C₄₁	—	2	2	no	—
120	C₂²⋊Q₈×C₄₁	—	2	2	no	—
121	C₂²⋊Q₈×C₄₁	—	2	2	no	—
122	C₂²⋊Q₈×C₄₁	—	2	2	no	—
123	C₂²⋊Q₈×C₄₁	—	2	1	no	—
124	C₂²⋊Q₈×C₄₁	—	2	1	no	—
125	C₂²⋊Q₈×C₄₁	—	2	1	no	—
126	C₂²⋊Q₈×C₄₁	—	2	1	no	—
127	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
128	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
129	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
130	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
131	#121×C₄₁	—	2	1	no	—
132	#121×C₄₁	—	2	1	no	—
133	#121×C₄₁	—	2	1	no	—
134	#121×C₄₁	—	2	1	no	—
135	#121×C₄₁	C₂³	1	2	yes	—
136	#121×C₄₁	C₂³	1	2	yes	—
137	#120×C₄₁	—	2	2	no	—
138	C₄×Q₈×C₄₁	—	2	2	no	—
139	C₄×Q₈×C₄₁	—	2	2	no	—
140	C₄×Q₈×C₄₁	—	2	2	no	—
141	C₄×Q₈×C₄₁	—	2	2	no	—
142	C₄×Q₈×C₄₁	—	2	2	no	—
143	C₄×Q₈×C₄₁	—	2	2	no	—
144	C₄×Q₈×C₄₁	—	2	1	no	—
145	C₄×Q₈×C₄₁	—	2	1	no	—
146	C₄×Q₈×C₄₁	—	2	1	no	—
147	C₄×Q₈×C₄₁	—	2	1	no	—
148	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
149	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
150	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
152	C₄×D₄×C₄₁	—	2	2	no	—
153	C₄×D₄×C₄₁	—	2	2	no	—
154	C₄×D₄×C₄₁	—	2	2	no	—
155	C₄×D₄×C₄₁	—	2	2	no	—
156	C₄×D₄×C₄₁	—	2	2	no	—
157	C₄×D₄×C₄₁	—	2	2	no	—
158	C₄×D₄×C₄₁	—	2	1	no	—
159	C₄×D₄×C₄₁	—	2	1	no	—
160	C₄×D₄×C₄₁	—	2	1	no	—
161	C₄×D₄×C₄₁	—	2	1	no	—
162	C₄×D₄×C₄₁	C₂³	1	2	yes	—
163	C₄×D₄×C₄₁	C₂³	1	2	yes	—
164	#117×C₄₁	—	2	2	no	—
165	#117×C₄₁	—	2	2	no	—
166	#117×C₄₁	—	2	2	no	—
167	#117×C₄₁	—	2	2	no	—
168	#117×C₄₁	—	2	1	no	—
169	#117×C₄₁	—	2	1	no	—
170	#117×C₄₁	—	2	2	no	—
171	#117×C₄₁	—	2	2	no	—
172	#117×C₄₁	—	2	2	no	—
173	#117×C₄₁	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
175	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
176	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
177	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
178	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
179	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
181	C₂×C₄²×C₄₁	—	2	2	no	—
182	C₂×C₄²×C₄₁	—	2	2	no	—
183	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
184	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
185	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
186	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
195	#107×C₄₁	C₂³	1	8	yes	—
196	#106×C₄₁	C₂³	1	8	yes	—
197	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
198	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
199	#103×C₄₁	C₂³	1	8	yes	—
200	#103×C₄₁	C₂³	1	8	yes	—
201	#103×C₄₁	C₂³	1	8	yes	—
202	#102×C₄₁	C₂³	1	8	yes	—
203	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
204	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
205	#97×C₄₁	C₂³	1	4	yes	—
206	#97×C₄₁	C₂³	1	4	yes	—
207	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
208	#41×C₄₁	—	4	4	no	—
209	#41×C₄₁	—	4	4	no	—
210	#41×C₄₁	—	4	4	no	—
211	C₂×Q₈×C₄₁	—	2	1	no	—
212	C₂×Q₈×C₄₁	—	2	1	no	—
213	C₂×Q₈×C₄₁	—	2	2	no	—
214	C₂×Q₈×C₄₁	—	2	2	no	—
215	C₂×Q₈×C₄₁	—	2	2	no	—
216	C₂×Q₈×C₄₁	—	4	4	no	—
217	C₂×Q₈×C₄₁	—	4	4	no	—
218	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
219	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
220	C₂×D₄×C₄₁	—	2	2	no	—
221	C₂×D₄×C₄₁	—	2	2	no	—
222	C₂×D₄×C₄₁	—	2	2	no	—
223	C₂×D₄×C₄₁	—	2	1	no	—
224	C₂×D₄×C₄₁	—	2	1	no	—
225	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₄₁	—	2	4	no	—
227	C₂²×C₄×C₄₁	—	2	2	no	—
228	C₂²×C₄×C₄₁	—	2	2	no	—
229	C₂²×C₄×C₄₁	—	2	2	no	—
230	C₂²×C₄×C₄₁	—	2	2	no	—
231	C₂²×C₄×C₄₁	—	2	2	no	—
232	C₂²×C₄×C₄₁	—	4	2	no	—
233	C₂²×C₄×C₄₁	—	4	2	no	—
234	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
252	Q₁₆×C₄₁	—	4	8	no	—
253	SD₁₆×C₄₁	—	4	8	no	—
254	C₂×C₈×C₄₁	—	4	4	no	—
255	C₂×C₈×C₄₁	C₂⁴	1	8	yes	—
256	C₄⋊C₄×C₄₁	—	2	2	no	—
257	C₄⋊C₄×C₄₁	—	2	2	no	—
258	C₄⋊C₄×C₄₁	—	2	2	no	—
259	C₄⋊C₄×C₄₁	—	2	2	no	—
260	C₄⋊C₄×C₄₁	—	2	2	no	—
261	C₄⋊C₄×C₄₁	—	2	2	no	—
262	C₄⋊C₄×C₄₁	—	2	4	no	—
263	C₄⋊C₄×C₄₁	—	2	4	no	—
264	C₄⋊C₄×C₄₁	—	2	4	no	—
265	C₄⋊C₄×C₄₁	—	2	4	no	—
266	C₄⋊C₄×C₄₁	—	2	2	no	—
267	C₄⋊C₄×C₄₁	—	2	1	no	—
268	C₄⋊C₄×C₄₁	—	2	1	no	—
269	C₄⋊C₄×C₄₁	—	2	1	no	—
270	C₄⋊C₄×C₄₁	—	2	1	no	—
271	C₄⋊C₄×C₄₁	—	2	2	no	—
272	C₄⋊C₄×C₄₁	—	2	2	no	—
273	C₄⋊C₄×C₄₁	—	2	2	no	—
274	C₄⋊C₄×C₄₁	—	2	2	no	—
275	C₄⋊C₄×C₄₁	—	2	2	no	—
276	C₄⋊C₄×C₄₁	—	2	2	no	—
277	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
278	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
279	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
280	C₂²⋊C₄×C₄₁	—	2	4	no	—
281	C₂²⋊C₄×C₄₁	—	2	4	no	—
282	C₂²⋊C₄×C₄₁	—	2	2	no	—
283	C₂²⋊C₄×C₄₁	—	2	2	no	—
284	C₂²⋊C₄×C₄₁	—	2	2	no	—
285	C₂²⋊C₄×C₄₁	—	2	2	no	—
286	C₂²⋊C₄×C₄₁	—	2	2	no	—
287	C₂²⋊C₄×C₄₁	—	2	2	no	—
288	C₂²⋊C₄×C₄₁	—	2	2	no	—
289	C₂²⋊C₄×C₄₁	—	2	2	no	—
290	C₂²⋊C₄×C₄₁	—	2	2	no	—
291	C₄²×C₄₁	—	2	2	no	—
292	C₄²×C₄₁	—	2	2	no	—
293	C₄²×C₄₁	—	2	4	no	—
294	C₄²×C₄₁	—	2	4	no	—
295	C₄²×C₄₁	—	2	2	no	—
296	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
297	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
300	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
309	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
310	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
311	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
312	C₂³×C₄₁	—	2	2	no	—
313	C₂³×C₄₁	—	2	2	no	—
314	C₂³×C₄₁	—	2	2	no	—
315	C₂³×C₄₁	—	4	1	no	—
316	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
317	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
318	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
319	Q₈×C₄₁	—	2	4	no	—
320	Q₈×C₄₁	—	2	4	no	—
321	Q₈×C₄₁	—	2	4	no	—
322	Q₈×C₄₁	—	4	4	no	—
323	Q₈×C₄₁	—	4	4	no	—
324	Q₈×C₄₁	—	4	4	no	—
325	Q₈×C₄₁	—	4	2	no	—
326	Q₈×C₄₁	—	4	2	no	—
327	D₄×C₄₁	—	2	4	no	—
328	D₄×C₄₁	—	4	2	no	—
329	D₄×C₄₁	—	4	4	no	—
330	D₄×C₄₁	—	4	4	no	—
331	D₄×C₄₁	—	4	4	no	—
332	D₄×C₄₁	—	4	2	no	—
333	C₂×C₄×C₄₁	—	2	2	no	—
334	C₂×C₄×C₄₁	—	2	2	no	—
335	C₂×C₄×C₄₁	—	2	2	no	—
336	C₂×C₄×C₄₁	—	2	2	no	—
337	C₂×C₄×C₄₁	—	2	2	no	—
338	C₂×C₄×C₄₁	—	2	2	no	—
339	C₂×C₄×C₄₁	—	2	2	no	—
340	C₂×C₄×C₄₁	—	2	2	no	—
341	C₂×C₄×C₄₁	—	2	2	no	—
342	C₂×C₄×C₄₁	—	2	2	no	—
343	C₂×C₄×C₄₁	—	2	2	no	—
344	C₂×C₄×C₄₁	—	2	2	no	—
345	C₂×C₄×C₄₁	—	2	2	no	—
346	C₂×C₄×C₄₁	—	2	4	no	—
347	C₂×C₄×C₄₁	—	2	4	no	—
348	C₂×C₄×C₄₁	—	4	1	no	—
349	C₂×C₄×C₄₁	—	4	1	no	—
350	C₂×C₄×C₄₁	—	4	1	no	—
351	C₂×C₄×C₄₁	—	4	1	no	—
352	C₂×C₄×C₄₁	—	4	1	no	—
353	C₂×C₄×C₄₁	—	4	1	no	—
354	C₂×C₄×C₄₁	—	4	1	no	—
355	C₂×C₄×C₄₁	—	4	4	no	—
356	C₂×C₄×C₄₁	—	4	4	no	—
357	C₂×C₄×C₄₁	—	4	4	no	—
358	C₂×C₄×C₄₁	—	4	4	no	—
359	C₂×C₄×C₄₁	—	4	4	no	—
360	C₂×C₄×C₄₁	#137	1	4	yes	—
361	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
362	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
364	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
366	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
367	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
368	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
371	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
372	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
373	C₈×C₄₁	—	2	8	no	—
374	#60963	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
375	C₂²×C₄₁	—	2	1	no	—
376	C₂²×C₄₁	—	2	1	no	—
377	C₂²×C₄₁	—	2	1	no	—
378	C₂²×C₄₁	—	2	1	no	—
379	C₂²×C₄₁	—	2	1	no	—
380	C₂²×C₄₁	—	2	1	no	—
381	C₂²×C₄₁	—	2	1	no	—
382	C₂²×C₄₁	—	4	4	no	—
383	C₂²×C₄₁	—	4	2	no	—
384	C₂²×C₄₁	—	4	2	no	—
385	C₂²×C₄₁	—	4	2	no	—
386	C₂²×C₄₁	C₂×#137	1	2	yes	—
387	C₂²×C₄₁	#575	1	2	yes	—
388	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
389	C₄×C₄₁	—	2	1	no	—
390	C₄×C₄₁	—	2	1	no	—
391	C₄×C₄₁	—	2	1	no	—
392	C₄×C₄₁	—	2	1	no	—
393	C₄×C₄₁	—	2	1	no	—
394	C₄×C₄₁	—	2	1	no	—
395	C₄×C₄₁	—	2	1	no	—
396	C₄×C₄₁	—	2	1	no	—
397	C₄×C₄₁	—	2	1	no	—
398	C₄×C₄₁	—	4	2	no	—
399	C₄×C₄₁	—	4	4	no	—
400	C₄×C₄₁	—	4	2	no	—
401	C₄×C₄₁	—	4	2	no	—
402	C₄×C₄₁	—	4	4	no	—
403	C₄×C₄₁	C₂×#137	1	2	yes	—
404	C₄×C₄₁	C₂×#137	1	2	yes	—
405	C₄×C₄₁	#585	1	2	yes	—
406	#3444	C₂×C₄₁	1	1	yes	characteristic
407	C₂×#533	C₂×C₄₁	1	1	yes	characteristic, complemented
408	#3249	C₂×C₄₁	1	2	yes	complemented
409	#3246	C₂×C₄₁	1	2	yes	complemented
410	#3238	C₂×C₄₁	1	2	yes	complemented
411	#3237	C₂×C₄₁	1	2	yes	complemented
412	#3218	C₂×C₄₁	1	2	yes	complemented
413	#3216	C₂×C₄₁	1	2	yes	complemented
414	#3190	C₂×C₄₁	1	4	yes	complemented
415	#3181	C₂×C₄₁	1	4	yes	complemented
416	#3116	C₂×C₄₁	1	4	yes	complemented
417	#3113	C₂×C₄₁	1	2	yes	complemented
418	#3112	C₂×C₄₁	1	2	yes	complemented
419	C₂×#432	C₂×C₄₁	1	1	yes	characteristic, complemented
420	C₂×C₄₁	—	2	2	no	—
421	C₂×C₄₁	—	2	2	no	—
422	C₂×C₄₁	—	4	1	no	—
423	C₂×C₄₁	—	8	2	no	—
424	C₂×C₄₁	#3449	1	1	yes	characteristic
425	C₂×C₄₁	C₂²×#137	1	1	yes	characteristic
426	C₂×C₄₁	C₂×#575	1	1	yes	characteristic
427	#533	—	2	1	no	—
428	#533	—	2	1	no	—
429	#533	—	2	1	no	—
430	#533	—	2	1	no	—
431	#533	C₂²×C₄₁	1	1	yes	characteristic
432	#533	C₂²×C₄₁	1	2	yes	—
433	#533	C₂²×C₄₁	1	2	yes	—
434	#533	C₂²×C₄₁	1	2	yes	—
435	#533	C₂²×C₄₁	1	2	yes	—
436	#533	C₂²×C₄₁	1	1	yes	characteristic
437	#533	C₂²×C₄₁	1	1	yes	characteristic
438	#532	C₂²×C₄₁	1	1	yes	characteristic
439	#532	C₂²×C₄₁	1	1	yes	characteristic
440	#532	C₂²×C₄₁	1	1	yes	characteristic
441	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
442	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
443	#529	—	2	1	no	—
444	#529	—	2	1	no	—
445	#529	—	2	1	no	—
446	#529	—	2	1	no	—
447	#529	C₂²×C₄₁	1	2	yes	—
448	#529	C₂²×C₄₁	1	2	yes	—
449	C₂×#125	—	2	1	no	—
450	#525	—	2	1	no	—
451	#525	—	2	1	no	—
452	#525	C₂²×C₄₁	1	2	yes	—
453	C₂×C₂²⋊Q₈	—	2	1	no	—
454	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
455	C₄×#41	—	2	1	no	—
456	C₄×#41	—	2	1	no	—
457	C₄×#41	C₂²×C₄₁	1	2	yes	—
458	C₂×C₄×Q₈	—	2	1	no	—
459	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
460	C₂×#117	—	2	1	no	—
461	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
462	#501	C₂²×C₄₁	1	4	yes	complemented
463	#497	C₂²×C₄₁	1	4	yes	complemented
464	#491	C₂²×C₄₁	1	4	yes	complemented
465	#489	C₂²×C₄₁	1	4	yes	complemented
466	#485	C₂²×C₄₁	1	8	yes	—
467	#483	C₂²×C₄₁	1	4	yes	—
468	#480	C₂²×C₄₁	1	4	yes	—
469	#477	C₂²×C₄₁	1	4	yes	complemented
470	#477	C₂²×C₄₁	1	4	yes	complemented
471	#476	C₂²×C₄₁	1	4	yes	complemented
472	#475	C₂²×C₄₁	1	4	yes	complemented
473	#467	C₂²×C₄₁	1	8	yes	—
474	#465	C₂²×C₄₁	1	8	yes	—
475	#462	C₂²×C₄₁	1	4	yes	complemented
476	#462	C₂²×C₄₁	1	4	yes	complemented
477	#461	C₂²×C₄₁	1	4	yes	complemented
478	#460	C₂²×C₄₁	1	4	yes	complemented
479	#452	C₂²×C₄₁	1	8	yes	—
480	#451	C₂²×C₄₁	1	4	yes	—
481	#448	C₂²×C₄₁	1	4	yes	—
482	#441	C₂²×C₄₁	1	8	yes	complemented
483	#440	C₂²×C₄₁	1	8	yes	complemented
484	#432	C₂²×C₄₁	1	2	yes	—
485	#432	C₂²×C₄₁	1	2	yes	—
486	#432	C₂²×C₄₁	1	2	yes	—
487	#432	C₂²×C₄₁	1	2	yes	—
488	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
489	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
490	C₂×#97	C₂²×C₄₁	1	2	yes	—
491	C₄₁	#60963	1	1	yes	characteristic, direct product factor, Sylow
492	C₂×#41	—	2	1	no	—
493	C₂×#41	—	2	1	no	—
494	C₂×#41	C₂³×C₄₁	1	2	yes	—
495	C₂²×Q₈	—	2	1	no	—
496	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
497	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
498	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
500	C₂×Q₁₆	C₂³×C₄₁	1	8	yes	—
501	C₂×SD₁₆	C₂³×C₄₁	1	8	yes	—
502	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
503	C₄⋊Q₈	—	2	1	no	—
504	C₄⋊Q₈	—	2	1	no	—
505	C₄⋊Q₈	—	2	1	no	—
506	C₄⋊Q₈	—	2	1	no	—
507	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
508	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
509	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
511	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
512	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
513	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
514	#127	C₂³×C₄₁	1	1	yes	characteristic
515	#126	—	2	2	no	—
516	#126	—	2	2	no	—
517	#125	—	2	2	no	—
518	#125	—	2	2	no	—
519	#125	—	2	2	no	—
520	#125	—	2	2	no	—
521	#125	—	2	1	no	—
522	#125	—	2	1	no	—
523	#125	C₂³×C₄₁	1	2	yes	—
524	#124	—	2	1	no	—
525	#124	—	2	1	no	—
526	#124	C₂³×C₄₁	1	2	yes	—
527	#123	—	2	2	no	—
528	#123	—	2	2	no	—
529	#123	—	2	2	no	—
530	C₂²⋊Q₈	—	2	2	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	2	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	—	2	1	no	—
538	C₂²⋊Q₈	—	2	1	no	—
539	C₂²⋊Q₈	—	2	1	no	—
540	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
541	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
542	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
543	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
544	#121	—	2	1	no	—
545	#121	—	2	1	no	—
546	#121	—	2	1	no	—
547	#121	—	2	1	no	—
548	#121	C₂³×C₄₁	1	2	yes	—
549	#121	C₂³×C₄₁	1	2	yes	—
550	#120	—	2	2	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	2	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	1	no	—
559	C₄×Q₈	—	2	1	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
562	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
563	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
564	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	2	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₄×D₄	—	2	2	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	1	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	C₂³×C₄₁	1	2	yes	—
576	C₄×D₄	C₂³×C₄₁	1	2	yes	—
577	#117	—	2	2	no	—
578	#117	—	2	2	no	—
579	#117	—	2	2	no	—
580	#117	—	2	2	no	—
581	#117	—	2	1	no	—
582	#117	—	2	1	no	—
583	#117	—	2	2	no	—
584	#117	—	2	2	no	—
585	#117	—	2	2	no	—
586	#117	C₂³×C₄₁	1	2	yes	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	1	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	2	no	—
591	C₂×C₄⋊C₄	—	2	2	no	—
592	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
593	C₂×C₂²⋊C₄	—	2	2	no	—
594	C₂×C₄²	—	2	2	no	—
595	C₂×C₄²	—	2	2	no	—
596	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
597	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
598	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
599	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
600	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
601	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
608	#107	C₂³×C₄₁	1	8	yes	—
609	#106	C₂³×C₄₁	1	8	yes	—
610	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
611	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
612	#103	C₂³×C₄₁	1	8	yes	—
613	#103	C₂³×C₄₁	1	8	yes	—
614	#103	C₂³×C₄₁	1	8	yes	—
615	#102	C₂³×C₄₁	1	8	yes	—
616	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
617	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
618	#97	C₂³×C₄₁	1	4	yes	—
619	#97	C₂³×C₄₁	1	4	yes	—
620	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
621	#41	—	4	4	no	—
622	#41	—	4	4	no	—
623	#41	—	4	4	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	2	2	no	—
628	C₂×Q₈	—	2	2	no	—
629	C₂×Q₈	—	4	4	no	—
630	C₂×Q₈	—	4	4	no	—
631	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
632	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
633	C₂×D₄	—	2	2	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	2	2	no	—
636	C₂×D₄	—	2	1	no	—
637	C₂×D₄	—	2	1	no	—
638	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	4	2	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
652	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
653	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
654	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
655	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
657	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
658	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
659	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
660	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
661	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
663	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
665	Q₁₆	—	4	8	no	—
666	SD₁₆	—	4	8	no	—
667	C₂×C₈	—	4	4	no	—
668	C₂×C₈	C₂⁴×C₄₁	1	8	yes	—
669	C₄⋊C₄	—	2	2	no	—
670	C₄⋊C₄	—	2	2	no	—
671	C₄⋊C₄	—	2	2	no	—
672	C₄⋊C₄	—	2	2	no	—
673	C₄⋊C₄	—	2	2	no	—
674	C₄⋊C₄	—	2	2	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	4	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	1	no	—
682	C₄⋊C₄	—	2	1	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	2	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
691	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
692	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	2	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₄²	—	2	2	no	—
705	C₄²	—	2	2	no	—
706	C₄²	—	2	4	no	—
707	C₄²	—	2	4	no	—
708	C₄²	—	2	2	no	—
709	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
710	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
711	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
712	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
713	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
714	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
715	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
716	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
717	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
718	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
719	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
720	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
721	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
722	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
723	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
724	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	4	1	no	—
729	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
730	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
731	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
732	Q₈	—	2	4	no	—
733	Q₈	—	2	4	no	—
734	Q₈	—	2	4	no	—
735	Q₈	—	4	4	no	—
736	Q₈	—	4	4	no	—
737	Q₈	—	4	4	no	—
738	Q₈	—	4	2	no	—
739	Q₈	—	4	2	no	—
740	D₄	—	2	4	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	4	no	—
743	D₄	—	4	4	no	—
744	D₄	—	4	4	no	—
745	D₄	—	4	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	2	4	no	—
761	C₂×C₄	—	4	1	no	—
762	C₂×C₄	—	4	1	no	—
763	C₂×C₄	—	4	1	no	—
764	C₂×C₄	—	4	1	no	—
765	C₂×C₄	—	4	1	no	—
766	C₂×C₄	—	4	1	no	—
767	C₂×C₄	—	4	1	no	—
768	C₂×C₄	—	4	4	no	—
769	C₂×C₄	—	4	4	no	—
770	C₂×C₄	—	4	4	no	—
771	C₂×C₄	—	4	4	no	—
772	C₂×C₄	—	4	4	no	—
773	C₂×C₄	#137×C₄₁	1	4	yes	—
774	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
775	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
776	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
777	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
778	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
779	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
780	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
781	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
782	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
783	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
784	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
785	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
786	C₈	—	2	8	no	—
787	C₂²	—	2	1	no	—
788	C₂²	—	2	1	no	—
789	C₂²	—	2	1	no	—
790	C₂²	—	2	1	no	—
791	C₂²	—	2	1	no	—
792	C₂²	—	2	1	no	—
793	C₂²	—	2	1	no	—
794	C₂²	—	4	4	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	C₂×#137×C₄₁	1	2	yes	—
799	C₂²	C₄₁×#575	1	2	yes	—
800	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
801	C₄	—	2	1	no	—
802	C₄	—	2	1	no	—
803	C₄	—	2	1	no	—
804	C₄	—	2	1	no	—
805	C₄	—	2	1	no	—
806	C₄	—	2	1	no	—
807	C₄	—	2	1	no	—
808	C₄	—	2	1	no	—
809	C₄	—	2	1	no	—
810	C₄	—	4	2	no	—
811	C₄	—	4	2	no	—
812	C₄	—	4	4	no	—
813	C₄	—	4	2	no	—
814	C₄	—	4	4	no	—
815	C₄	C₂×#137×C₄₁	1	2	yes	—
816	C₄	C₂×#137×C₄₁	1	2	yes	—
817	C₄	C₄₁×#585	1	2	yes	—
818	C₂	—	2	2	no	—
819	C₂	—	2	2	no	—
820	C₂	—	4	1	no	—
821	C₂	—	8	2	no	—
822	C₂	C₄₁×#3449	1	1	yes	characteristic
823	C₂	C₂²×#137×C₄₁	1	1	yes	characteristic
824	C₂	C₂×C₄₁×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₄₁×#533	C₂	semidirect
3. C₄₁×#3249	C₂	semidirect
4. C₄₁×#3246	C₂	semidirect
5. C₄₁×#3238	C₂	semidirect
6. C₄₁×#3237	C₂	semidirect
7. C₄₁×#3218	C₂	semidirect
8. C₄₁×#3216	C₂	semidirect
9. C₄₁×#3190	C₂	semidirect
10. C₄₁×#3181	C₂	semidirect
11. C₄₁×#3116	C₂	semidirect
12. C₄₁×#3113	C₂	semidirect
13. C₄₁×#3112	C₂	semidirect
14. C₂×C₄₁×#432	C₂	semidirect
50. C₄₁×#501	C₂²	semidirect
51. C₄₁×#497	C₂²	semidirect
52. C₄₁×#491	C₂²	semidirect
53. C₄₁×#489	C₂²	semidirect
57. C₄₁×#477	C₂²	semidirect
58. C₄₁×#477	C₂²	semidirect
59. C₄₁×#476	C₂²	semidirect
60. C₄₁×#475	C₂²	semidirect
63. C₄₁×#462	C₂²	semidirect
64. C₄₁×#462	C₂²	semidirect
65. C₄₁×#461	C₂²	semidirect
66. C₄₁×#460	C₂²	semidirect
70. C₄₁×#441	C₂²	semidirect
71. C₄₁×#440	C₂²	semidirect
374. #60963	C₄₁	direct (N × H)
407. C₂×#533	C₂×C₄₁	semidirect
408. #3249	C₂×C₄₁	semidirect
409. #3246	C₂×C₄₁	semidirect
410. #3238	C₂×C₄₁	semidirect
411. #3237	C₂×C₄₁	semidirect
412. #3218	C₂×C₄₁	semidirect
413. #3216	C₂×C₄₁	semidirect
414. #3190	C₂×C₄₁	semidirect
415. #3181	C₂×C₄₁	semidirect
416. #3116	C₂×C₄₁	semidirect
417. #3113	C₂×C₄₁	semidirect
418. #3112	C₂×C₄₁	semidirect
419. C₂×#432	C₂×C₄₁	semidirect
462. #501	C₂²×C₄₁	semidirect
463. #497	C₂²×C₄₁	semidirect
464. #491	C₂²×C₄₁	semidirect
465. #489	C₂²×C₄₁	semidirect
469. #477	C₂²×C₄₁	semidirect
470. #477	C₂²×C₄₁	semidirect
471. #476	C₂²×C₄₁	semidirect
472. #475	C₂²×C₄₁	semidirect
475. #462	C₂²×C₄₁	semidirect
476. #462	C₂²×C₄₁	semidirect
477. #461	C₂²×C₄₁	semidirect
478. #460	C₂²×C₄₁	semidirect
482. #441	C₂²×C₄₁	semidirect
483. #440	C₂²×C₄₁	semidirect
491. C₄₁	#60963	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₁×#3444	2
C₂×C₄₁×#533	2
C₄₁×#3249	2
C₄₁×#3246	2
C₄₁×#3238	2
C₄₁×#3237	2
C₄₁×#3218	2
C₄₁×#3216	2
C₄₁×#3190	2
C₄₁×#3181	2
C₄₁×#3116	2
C₄₁×#3113	2
C₄₁×#3112	2
C₂×C₄₁×#432	2
#60963	41

Subgroups — C41×#60963 #23837164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#60963 #23837164